Finite Group Databasebeta

C2×#31775937 #46855046

order35008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31775937

Splittings

SylowC547 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D547
commutatorC4×C547C22×C4
FrattiniC2×C4C22×D547
FittingC2×M16×C547C2
socleC22×C547C4⋊C4
prime radicalC23×C547Q8
cosocleC2×C4×C547C23
hypercenterC2×M16D547
hypocenterC547C2×#108
LCSG ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17504

Conjugacy classes & character table

5488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35008, 594);