Finite Group Databasebeta

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C2×C3×C7×C8×C32 #72189296

order10752
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 786432
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C8

Aliases

abelianC2×C3×C7×C8×C32
multiplicative(ℤ/21536)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C16C23×C3×C7
socle, prime radicalC23×C3×C7C4×C16
LCSG ▷ C1
UCSC1 ◁ G

1032 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C7×C8×C64, C2×C3×C7×C16×C32, C3×C4×C7×C8×C32, …
maximal normal subgroup ofC2×C3×C7×C8×C64, C2×C3×C7×C16×C32, C3×C4×C7×C8×C32, …
maximal quotient ofC2×C3×C7×C8×C64, C2×C3×C7×C16×C32, C3×C4×C7×C8×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.