Finite Group Databasebeta

C2×#28417888 #44470082

order29888
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28417888

Splittings

SylowC467 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D467
commutatorC4×C467C22×C4
FrattiniC2×C4C22×D467
FittingC2×M16×C467C2
socleC22×C467C4⋊C4
prime radicalC23×C467Q8
cosocleC2×C4×C467C23
hypercenterC2×M16D467
hypocenterC467C2×#108
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Conjugacy classes & character table

4688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 594);