Finite Group Databasebeta

← Prev (#28588226) Next (#28588228) →

C2×#21424117 #28588227

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

Aliases

direct productC2×#21424117

Splittings

FittingC2×C4×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C2×#1806

Subgroups

subgroupG/H
centerC22×C4C2×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C4×C4⋊C4×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenterC2×C4×C4⋊C4D59
hypocenterC59C2×#1806
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1618 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, 169106);