Finite Group Databasebeta

C2×#21424999 #28592675

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

Aliases

direct productC2×#21424999

Splittings

FittingC2×C59×#405 ⋊ C2
SylowC59 ⋊ C2×#1977

Subgroups

subgroupG/H
centerC23#14273701
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#405C2
socleC23×C59#121
prime radicalC23×D236C22
cosocleC22×C4×C59C24
hypercenterC2×#405D59
hypocenterC59C2×#1977
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#405

1566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 173554);