Finite Group Databasebeta

C2×#21426005 #28742177

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21426005

Splittings

SylowC59 ⋊ C2×#2183

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC22×C59C23×C8
FrattiniC2×C8C23×D59
FittingC2×C8×Q8×C59C2
socle, prime radicalC23×C59C22×C8
cosocleC2×C8×C59C24
hypercenterC2×C8×Q8D59
hypocenterC59C2×#2183
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323056);