Finite Group Databasebeta

C2×#27189653 #39909293

order26176
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27189653

Splittings

SylowC409 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1636
commutatorC4×C409C22×C4
FrattiniC2×C4C22×D409
FittingC22×C8×C409C2
socleC22×C409C4⋊C4
prime radicalC23×C409Q8
cosocleC2×C4×C409C23
hypercenterC22×C8D409
hypocenterC409C2×#108
LCSG ▷ C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

6556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 595);