Finite Group Databasebeta

C2×#22564024 #31023323

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22564024

Splittings

SylowC67 ⋊ C2×#2449

Subgroups

subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#386×C67C2
socleC24×C67C24
prime radicalC23×D4×C67C22
hypercenterC2×#386D67
hypocenterC67C2×#2449
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#386

3830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 337060);