Finite Group Databasebeta

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C2×C72×C8×C11 #72187463

order8624
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 322560
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C7

Aliases

abelianC2×C72×C8×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C72×C11
socle, prime radicalC22×C72×C11C4
LCSG ▷ C1
UCSC1 ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C72×C11×C16, C4×C72×C8×C11, C22×C72×C8×C11, …
maximal normal subgroup ofC2×C72×C11×C16, C4×C72×C8×C11, C22×C72×C8×C11, …
maximal quotient ofC2×C72×C11×C16, C4×C72×C8×C11, C22×C72×C8×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.