Finite Group Databasebeta

C2×#22563503 #31022112

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22563503

Splittings

SylowC67 ⋊ C2×#2399

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×C4×C4⋊C4×C67C2
socle, prime radicalC24×C67C24
hypercenterC2×C4×C4⋊C4D67
hypocenterC67C2×#2399
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 335849);