Finite Group Databasebeta

C2×#21422538 #28555105

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

Aliases

direct productC2×#21422538

Splittings

FittingC2×C59×#432 ⋊ C2
SylowC59 ⋊ C2×#1490

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC2×C59×#432C2
socleC23×C59C2×C22⋊C4
prime radicalC23×D236C4
cosocleC42×C59C24
hypercenterC2×#432D59
hypocenterC59C2×#1490
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#432

1734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 135984);