Finite Group Databasebeta

C2×#21424433 #28590008

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21424433

Splittings

FittingC2×C59×#391 ⋊ C2
SylowC59 ⋊ C2×#1877

Subgroups

subgroupG/H
centerC24C2×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#391C2
socleC24×C59C2×D4
prime radicalC23×D236C22
cosocleC22×C4×C59C24
hypercenterC2×#391D59
hypocenterC59C2×#1877
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#391

2254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 170887);