Finite Group Databasebeta

C2×#22559077 #30825375

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22559077

Splittings

SylowC67 ⋊ C2×#1587

Subgroups

subgroupG/H
centerC22×C4D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC42C23×D67
FittingC2×Q8⋊C8×C67C2
socle, prime radicalC23×C67C4×D4
cosocleC42×C67C24
hypercenterC2×Q8⋊C8D67
hypocenterC67C2×#1587
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 139112);