Finite Group Databasebeta

C2×#21421982 #28478809

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#21421982

Splittings

SylowC59 ⋊ C2×#1297

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC2×C4×C22⋊C4×C59C2
socleC23×C59#95
prime radicalC25×C59D4
cosocleC23×C4×C59C23
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C2×#1297
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59688);