Finite Group Databasebeta

C2×#21422173 #28503525

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21422173

Splittings

SylowC59 ⋊ C2×#1374

Subgroups

subgroupG/H
centerC23×C8C2×D59
commutatorC2×C59C2×C4×C16
FrattiniC22×C8C22×D59
FittingC23×C16×C59C2
socle, prime radicalC24×C59C2×C8
cosocleC22×C8×C59C23
hypercenterC23×C16D59
hypocenterC59C2×#1374
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C8 ◁ C23×C16

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84404);