Finite Group Databasebeta

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C22×C32×C8×C23 #72185752

order6624
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 405504
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C32×C8×C23

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C32×C23
socle, prime radicalC23×C32×C23C4
LCSG ▷ C1
UCSC1 ◁ G

456 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C16×C23, C2×C32×C4×C8×C23, C23×C32×C8×C23, …
maximal normal subgroup ofC22×C32×C16×C23, C2×C32×C4×C8×C23, C23×C32×C8×C23, …
maximal quotient ofC22×C32×C16×C23, C2×C32×C4×C8×C23, C23×C32×C8×C23, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.