Finite Group Databasebeta

C4×#16837874 #28746922

order15104
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#16837874

Splittings

FittingC42×D4×C59 ⋊ C2
SylowC59 ⋊ C4×#518

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC2×C59C23×C42
FrattiniC23C24×D59
FittingC42×D4×C59C2
socle, cosocleC23×C59C25
prime radicalC22×D4×D59C22
hypercenterC42×D4D59
hypocenterC59C4×#518
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C42×D4

4186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 327801);