Finite Group Databasebeta

C4×#16837677 #28595580

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#16837677

Splittings

SylowC59 ⋊ C4×#473

Subgroups

subgroupG/H
centerC2×C4#14273701
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×#131×C59C2
socleC22×C59C2×#121
prime radicalC2×#41×C59C23
cosocleC22×C4×C59C24
hypercenterC4×#131D59
hypocenterC59C4×#473
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#131

882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 176459);