Finite Group Databasebeta

C2×#27211945 #41001574

order26848
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27211945

Splittings

SylowC839 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22C22⋊D839
commutator, cosocleC4×C839C23
FrattiniC4C22×D839
FittingC2×Q8×C839C2
socle, prime radicalC22×C839D4
hypercenterC2×Q8D839
hypocenterC839C2×Q16
LCSG ▷ C4×C839 ▷ C2×C839 ▷ C839
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26848

Conjugacy classes & character table

4204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26848, 163);