Finite Group Databasebeta

C4×#16837408 #28586467

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

Aliases

direct productC4×#16837408

Splittings

FittingC2×C4×M16×C59 ⋊ C2
SylowC59 ⋊ C4×#418

Subgroups

subgroupG/H
centerC22×C4C2×D236
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC2×C4×M16×C59C2
socleC23×C59C22×D4
prime radicalC23×D236C22
cosocleC22×C4×C59C24
hypercenterC2×C4×M16D59
hypocenterC59C4×#418
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

2018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 167346);