Finite Group Databasebeta

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C4×C5×C72×C11 #24924724

order10780
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 161280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C7

Aliases

abelianC4×C5×C72×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C5×C72×C11
socle, prime radicalC2×C5×C72×C11C2
LCSG ▷ C1
UCSC1 ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10780 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC4×C5×C11×#3862, C4×C5×C7×C11×ΓL(1,𝔽8), C4×C5×C11×#3861
maximal subgroup ofC3×C4×C5×C72×C11, C4×C5×C11×#3862, C4×C5×C7×C11×ΓL(1,𝔽8), …
maximal normal subgroup ofC3×C4×C5×C72×C11, C4×C5×C11×#3862, C4×C5×C7×C11×ΓL(1,𝔽8), …
maximal quotient ofC3×C4×C5×C72×C11, C5×C72×C11×Dic3, C5×C72×C8×C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 37);