Finite Group Databasebeta

C2×#30660372 #45690748

order33472
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#30660372

Splittings

SylowC523 ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
centerC23C22×D523
commutator, cosocleC22×C523C24
FrattiniC22C23×D523
FittingC2×C4⋊C4×C523C2
socle, prime radicalC23×C523C23
hypercenterC2×C4⋊C4D523
hypocenterC523C2×C4⋊Q8
LCSG ▷ C22×C523 ▷ C523
UCSC1 ◁ C23 ◁ C2×C4⋊C4

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33472

Conjugacy classes & character table

5248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 1092);