Finite Group Databasebeta

C2×#21422055 #28498405

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

Aliases

direct productC2×#21422055

Splittings

FittingC2×C59×#346 ⋊ C2
SylowC59 ⋊ C2×#1330

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC2×C4×C59C22×C8
FrattiniC4×C8C22×D59
FittingC2×C59×#346C2
socleC23×C59C22⋊C8
prime radicalC22×D236C8
cosocleC4×C8×C59C23
hypercenterC2×#346D59
hypocenterC59C2×#1330
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#346

422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 79284);