Finite Group Databasebeta

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C22⋊C4×Dic166 #24910298

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

Aliases

direct productC22⋊C4×Dic166

Splittings

SylowC83 ⋊ Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D83
commutatorC22×C83C23×C4
FittingC4×C22⋊C4×C83C2
socle, cosocleC23×C83C24
prime radicalC24×C83C23
hypercenterC4×C22⋊C4D83
hypocenterC83Q8×C22⋊C4
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C22⋊C4

820 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#35300843, #35300847, #35300871, …
maximal normal subgroup of#35300843, #35300847, #35300871, …
maximal quotient ofC22⋊C4×C4⋊Dic83, C22⋊C4×Dic83⋊C4, #95×Dic166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 7345);