Finite Group Databasebeta

C2×#30660319 #45690632

order33472
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30660319

Splittings

SylowC523 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#22552626
commutator, cosocleC8×C523C23
FrattiniC8C22×D523
FittingC2×Q16×C523C2
socle, prime radicalC22×C523D8
hypercenterC2×Q16D523
hypocenterC523C2×Q32
LCSG ▷ C8×C523 ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33472

Conjugacy classes & character table

3676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 976);