Finite Group Databasebeta

C2×#21432977 #29452850

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21432977

Splittings

FittingC2×C59×#520 ⋊ C2
SylowC59 ⋊ C2×#2952

Subgroups

subgroupG/H
centerC23C22×C22⋊D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#520C2
socleC23×C59C22×D4
prime radicalC22×#14273747C2
cosocleC2×C4×C59C25
hypercenterC2×#520D59
hypocenterC59C2×#2952
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

2806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033729);