Finite Group Databasebeta

C2×#21422202 #28503604

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21422202

Splittings

SylowC59 ⋊ C2×#1386

Subgroups

subgroupG/H
centerC23#14273649
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC22×M32×C59C2
socleC23×C59#102
prime radicalC24×C59D8
cosocleC22×C8×C59C23
hypercenterC22×M32D59
hypocenterC59C2×#1386
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

630 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, 84483);