Finite Group Databasebeta

C2×#28414206 #44443153

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

Aliases

direct productC2×#28414206

Splittings

SylowC461 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#14270406
commutatorC2×C461C23×C4
FrattiniC2C23×#14270406
FittingC2×Q8×C461C4
socleC22×C461C22×C4
prime radicalC2×#20301502C2
cosocleDic461C24
hypercenterC2×Q8#14270406
hypocenterC461C2×#131
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1626);