Finite Group Databasebeta

C2×#28414179 #44443060

order29504
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28414179

Splittings

SylowC461 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊#14270406
commutatorC22×C461C22×C4
FrattiniC22C22×#14270406
FittingC22×C4×C461C4
socleC22×C461C22⋊C4
prime radicalC23×C461C2×C4
cosocleC2×Dic461C23
hypercenterC22×C4#14270406
hypocenterC461C2×#101
LCSG ▷ C22×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

1862 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1533);