Finite Group Databasebeta

C2×#28410469 #44416754

order29248
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28410469

Splittings

SylowC457 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic457
commutatorC22×C457C22×C4
FrattiniC2×C4C22×D457
Fitting, prime radicalC22×D4×C457C2
socleC22×C457C22⋊C4
cosocleC2×C4×C457C23
hypercenterC22×D4D457
hypocenterC457C2×#100
LCSG ▷ C22×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7312

Conjugacy classes & character table

4582 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 526);