Finite Group Databasebeta

C2×#21425749 #28741425

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

Aliases

direct productC2×#21425749

Splittings

SylowC59 ⋊ C2×#2123

Subgroups

subgroupG/H
centerC22C2×#14273641
commutatorC23×C59C23×C4
FrattiniC2×D4C23×D59
FittingC2×C59×#410C2
socleC22×C59C2×#99
prime radicalC22×#41×C59C22
cosocleC2×D4×C59C24
hypercenterC2×#410D59
hypocenterC59C2×#2123
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1322 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322304);