Finite Group Databasebeta

C2×#30659796 #45688509

order33344
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#30659796

Splittings

SylowC521 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#14523438
commutatorC2×C521C23×C4
FrattiniC2C23×#14523438
FittingC2×Q8×C521C4
socleC22×C521C22×C4
prime radicalC2×#22552365C2
cosocleDic521C24
hypercenterC2×Q8#14523438
hypocenterC521C2×#131
LCSG ▷ C2×C521 ▷ C521
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16672

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33344, 1626);