Finite Group Databasebeta

C2×#28410559 #44417540

order29248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28410559

Splittings

SylowC457 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D457
commutatorC2×C457C23×C4
FrattiniC4C23×D457
Fitting, prime radicalC2×#41×C457C2
socleC22×C457C22×C4
cosocleC4×C457C24
hypercenterC2×#41D457
hypocenterC457C2×#131
LCSG ▷ C2×C457 ▷ C457
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14624

Conjugacy classes & character table

4600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 1312);