Finite Group Databasebeta

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C32×C7×C5⋊D5 #15691304

order3150
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3×C5

Aliases

direct productC32×C7×C5⋊D5
unambiguous semidirect productC5⋊(C32×C7×D5)

Splittings

Fitting, socle, HallC32×C52×C7 ⋊ C2
derived, SylowC52 ⋊ C2×C32×C7
HallC32×C52 ⋊ C2×C7
HallC52×C7 ⋊ C2×C32

Subgroups

subgroupG/H
center, hypercenterC32×C7C5⋊D5
commutator, cosocle, hypocenterC52C2×C32×C7
FrattiniC1G
Fitting, socleC32×C52×C7C2
LCSG ▷ C52
UCSC1 ◁ C32×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 1575

A minimal faithful permutation representation — 3 generators on 23 points:

(1,2,3)(7,8,9,10,11,12,13)(15,16)(17,18)(20,21)(22,23);(4,5,6)(19,20,22,23,21);(14,15,17,18,16)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC32×C49×C5⋊D5, C3×C7×ΓL(1,𝔽8)×C5⋊D5, C3×C7×C5⋊(C5⋊AGL(1,𝔽7)), …
maximal normal subgroup ofC32×C49×C5⋊D5, C32×C72×C5⋊D5, C32×C7×C11×C5⋊D5
maximal quotient ofC32×C49×C5⋊D5, C3×C7×ΓL(1,𝔽8)×C5⋊D5, C3×C7×C5⋊(C5⋊AGL(1,𝔽7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3150, 103);