Finite Group Databasebeta

C2×#28414053 #44442121

order29504
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28414053

Splittings

SylowC461 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D461
commutatorC4×C461C22×C4
FrattiniC2×C4C22×D461
FittingC2×M16×C461C2
socleC22×C461C4⋊C4
prime radicalC23×C461Q8
cosocleC2×C4×C461C23
hypercenterC2×M16D461
hypocenterC461C2×#108
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

4628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 594);