Finite Group Databasebeta

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C4×#19149657 #36356096

order22144
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#19149657

Splittings

FittingC4×C4⋊C4×C173 ⋊ C2
SylowC173 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D173
commutatorC22×C173C23×C4
FrattiniC23C23×D173
FittingC4×C4⋊C4×C173C2
socle, cosocleC23×C173C24
prime radicalC23×D173C23
hypercenterC4×C4⋊C4D173
hypocenterC173C4×C22⋊Q8
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11072

Conjugacy classes & character table

3496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 7043);