Finite Group Databasebeta

C2×#28414125 #44442839

order29504
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28414125

Splittings

SylowC461 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D461
commutatorC2×C461C23×C4
FrattiniC4C23×D461
Fitting, prime radicalC2×#41×C461C2
socleC22×C461C22×C4
cosocleC4×C461C24
hypercenterC2×#41D461
hypocenterC461C2×#131
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

4640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1312);