Finite Group Databasebeta

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C4⋊C4×C22⋊D181 #37536620

order23168
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×C22⋊D181

Splittings

FittingC22×C4⋊C4×C181 ⋊ C2
SylowC181 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
FittingC22×C4⋊C4×C181C2
socle, cosocleC23×C181C24
prime radicalC22×C22⋊D181C22
hypercenterC22×C4⋊C4D181
hypocenterC181D4×C4⋊C4
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ C22×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11584

Conjugacy classes & character table

3650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 7409);