Finite Group Databasebeta

C2×#21433014 #29453011

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21433014

Splittings

FittingC2×C59×#405 ⋊ C2
SylowC59 ⋊ C2×#2957

Subgroups

subgroupG/H
centerC2×C4C22×D236
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#405C2
socleC22×C59C2×C4×D4
prime radicalC22×#14273749C2
cosocleC2×C4×C59C25
hypercenterC2×#405D59
hypocenterC59C2×#2957
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×#405

2642 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, 1033890);