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C22×C82×C29 #20312210

order7424
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 66060288
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C8

Aliases

abelianC22×C82×C29
multiplicative(ℤ/22368)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC42C24×C29
socleC24×C29C42
LCSG ▷ C1
UCSC1 ◁ G

1342 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C8×C16×C29, C2×C4×C82×C29, C23×C82×C29, …
maximal normal subgroup ofC22×C8×C16×C29, C2×C4×C82×C29, C23×C82×C29, …
maximal quotient ofC22×C8×C16×C29, C2×C4×C82×C29, C23×C82×C29, …
automorphism group ofC3×C32×C233
outer automorphism group ofC3×C32×C233

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 10298);