Finite Group Databasebeta

C2×#21422189 #28503575

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

Aliases

direct productC2×#21422189

Splittings

SylowC59 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC22×C4#11745669
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC22×#108×C59C2
socleC23×C59#107
prime radicalC24×C59Q16
cosocleC22×C8×C59C23
hypercenterC22×#108D59
hypocenterC59C2×#1381
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84454);