Finite Group Databasebeta

C2×#28414083 #44442540

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

Aliases

direct productC2×#28414083

Splittings

SylowC461 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D461
commutatorC2×C461C23×C4
FrattiniC22C23×D461
FittingC2×C4⋊C4×C461C2
socle, prime radicalC23×C461C23
cosocleC22×C461C24
hypercenterC2×C4⋊C4D461
hypocenterC461C2×C4×Q8
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C23 ◁ C2×C4⋊C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29504

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, 1013);