Finite Group Databasebeta

C2×#21424148 #28588349

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21424148

Splittings

SylowC59 ⋊ C2×#1814

Subgroups

subgroupG/H
centerC2×C4#14273699
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#421C2
socleC22×C59#380
prime radicalC22×#41×C59C22
cosocleC22×C4×C59C24
hypercenterC2×#421D59
hypocenterC59C2×#1814
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

1330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 169228);