Finite Group Databasebeta

C2×#21422087 #28498843

order15104
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21422087

Splittings

SylowC59 ⋊ C2×#1341

Subgroups

subgroupG/H
centerC22#16837136
commutatorC2×C8×C59C22×C4
FrattiniC2×M16C22×D59
Fitting, prime radicalC2×C59×#469C2
socleC22×C59#327
cosocleC2×M16×C59C23
hypercenterC2×#469D59
hypocenterC59C2×#1341
LCSG ▷ C2×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#469

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 79722);