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C3×C5×C11×Dic7 #17987609

order4620
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×Dic7

Splittings

derived, SylowC7 ⋊ C3×C4×C5×C11
HallC3×C5×C7×C11 ⋊ C4
HallC5×C7×C11 ⋊ C3×C4
HallC3×C7×C11 ⋊ C4×C5
HallC3×C5×C7 ⋊ C4×C11
HallC7×C11 ⋊ C3×C4×C5
HallC5×C7 ⋊ C3×C4×C11
HallC3×C7 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11D7
commutator, hypocenterC7C3×C4×C5×C11
FrattiniC2C3×C5×C11×D7
Fitting, socle, prime radicalC2×C3×C5×C7×C11C2
cosocleC2×C7C2×C3×C5×C11
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 4620

A minimal faithful permutation representation — 2 generators on 30 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);(20,22,21,23)(25,30)(26,29)(27,28)

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×C11×Dic7, C5×C11×Dic7⋊C9, C3×C5×C11×ΓL(1,𝔽8)⋊C4, …
maximal normal subgroup ofC5×C9×C11×Dic7, C5×C11×Dic7⋊C9, C3×C5×C11×ΓL(1,𝔽8)⋊C4, …
maximal quotient ofC5×C9×C11×Dic7, C32×C5×C11×Dic7, C3×C5×C11×Dic21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 6);