Finite Group Databasebeta

C2×#21422539 #28555106

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

Aliases

direct productC2×#21422539

Splittings

SylowC59 ⋊ C2×#1490

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC22×C4×D4×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC23×D4×C59C4
cosocleC42×C59C24
hypercenterC22×C4×D4D59
hypocenterC59C2×#1490
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×D4

1734 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, 135985);