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C3×C7×D115 #18012575

order4830
isoclinismisoclinic class of D115
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D115
unambiguous semidirect productC5⋊(C3×C7×D23)
unambiguous semidirect productC23⋊(C3×C7×D5)

Splittings

Fitting, socle, HallC3×C5×C7×C23 ⋊ C2
derived, HallC5×C23 ⋊ C2×C3×C7
HallC5×C7×C23 ⋊ C2×C3
HallC3×C7×C23 ⋊ D5
HallC3×C5×C23 ⋊ C2×C7
HallC7×C23 ⋊ C3×D5
HallC3×C5×C7 ⋊ D23
HallC3×C23 ⋊ C7×D5
HallC5×C7 ⋊ C3×D23
SylowC23 ⋊ C3×C7×D5
HallC3×C5 ⋊ C7×D23
SylowC5 ⋊ C3×C7×D23

Subgroups

subgroupG/H
center, hypercenterC3×C7D115
commutator, cosocle, hypocenterC5×C23C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C23C2
LCSG ▷ C5×C23
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 2415

A minimal faithful permutation representation — 2 generators on 38 points:

(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38);(12,15)(13,14)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C9×D115, C7⋊C9×D115, C3×ΓL(1,𝔽8)×D115, …
maximal normal subgroup ofC7×C9×D115, C7⋊C9×D115, C3×ΓL(1,𝔽8)×D115, …
maximal quotient ofC7×C9×D115, C3×C7×D345, C32×C7×D115, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4830, 7);