Finite Group Databasebeta

C2×#27210663 #40997482

order26528
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27210663

Splittings

SylowC829 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22C22⋊D829
commutator, cosocleC4×C829C23
FrattiniC4C22×D829
FittingC2×Q8×C829C2
socle, prime radicalC22×C829D4
hypercenterC2×Q8D829
hypocenterC829C2×Q16
LCSG ▷ C4×C829 ▷ C2×C829 ▷ C829
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26528

Conjugacy classes & character table

4154 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26528, 163);