Finite Group Databasebeta

C2×#21422214 #28503628

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21422214

Splittings

SylowC59 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC23#14273642
commutatorC23×C59C2×C42
FrattiniC22×D4C22×D59
FittingC2×C59×#386C2
socleC23×C59#99
prime radicalC23×D4×C59C22
cosocleC22×D4×C59C23
hypercenterC2×#386D59
hypocenterC59C2×#1390
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C2×#386

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84507);