Finite Group Databasebeta

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C4⋊C4×#11745659 #28586677

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4⋊C4×#11745659

Splittings

FittingC8×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D59
commutatorC22×C59C22×C42
FittingC8×C4⋊C4×C59C2
socleC23×C59C23×C4
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenterC8×C4⋊C4D59
hypocenterC59C4⋊C4×M16
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C8×C4⋊C4

1242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 167556);