Finite Group Databasebeta

C2×#27165672 #38786159

order25664
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27165672

Splittings

SylowC401 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D401
commutatorC4×C401C22×C4
FrattiniC2×C4C22×D401
FittingC2×M16×C401C2
socleC22×C401C4⋊C4
prime radicalC23×C401Q8
cosocleC2×C4×C401C23
hypercenterC2×M16D401
hypocenterC401C2×#108
LCSG ▷ C4×C401 ▷ C2×C401 ▷ C401
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12832

Conjugacy classes & character table

4028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25664, 594);