Finite Group Databasebeta

C2×#30660309 #45690251

order33472
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30660309

Splittings

SylowC523 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D2092
commutatorC4×C523C22×C4
FrattiniC2×C4C22×D523
FittingC22×C8×C523C2
socleC22×C523C4⋊C4
prime radicalC23×C523Q8
cosocleC2×C4×C523C23
hypercenterC22×C8D523
hypocenterC523C2×#108
LCSG ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16736

Conjugacy classes & character table

8380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 595);