Finite Group Databasebeta

C2×#27211653 #41000406

order26816
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27211653

Splittings

SylowC419 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D419
commutatorC4×C419C22×C4
FrattiniC2×C4C22×D419
FittingC2×M16×C419C2
socleC22×C419C4⋊C4
prime radicalC23×C419Q8
cosocleC2×C4×C419C23
hypercenterC2×M16D419
hypocenterC419C2×#108
LCSG ▷ C4×C419 ▷ C2×C419 ▷ C419
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13408

Conjugacy classes & character table

4208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 594);