Finite Group Databasebeta

C2×#21422168 #28500267

order15104
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21422168

Splittings

SylowC59 ⋊ C2×#1371

Subgroups

subgroupG/H
centerC22×C4D472
commutatorC8×C59C22×C8
FrattiniC4×C8C22×D59
FittingC2×C4×C16×C59C2
socle, prime radicalC23×C59#107
cosocleC4×C8×C59C23
hypercenterC2×C4×C16D59
hypocenterC59C2×#1371
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 81146);