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C4⋊C4×Dic178 #26023167

order11392
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic178

Splittings

SylowC89 ⋊ Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D89
commutatorC22×C89C23×C4
FittingC4×C4⋊C4×C89C2
socle, prime radical, cosocleC23×C89C24
hypercenterC4×C4⋊C4D89
hypocenterC89Q8×C4⋊C4
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C4×C4⋊C4

568 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1810 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36448601, #36448605, #36448629, …
maximal normal subgroup of#36448601, #36448605, #36448629, …
maximal quotient ofC4⋊C4×#13083553, C4⋊C4×C4⋊Dic89, #95×Dic178, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7425);