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C4⋊C4×D332 #24910366

order10624
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×D332

Splittings

FittingC4×C4⋊C4×C83 ⋊ C2
SylowC83 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D83
commutatorC22×C83C23×C4
FittingC4×C4⋊C4×C83C2
socle, cosocleC23×C83C24
prime radicalC22×D332C22
hypercenterC4×C4⋊C4D83
hypocenterC83D4×C4⋊C4
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1690 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35298563, #35298567, #35298591, …
maximal normal subgroup of#35298563, #35298567, #35298591, …
maximal quotient ofC4⋊C4×(C2×D83)⋊C4, C4⋊C4×C4⋊Dic83, #95×D332, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 7413);