Finite Group Databasebeta

C2×Dic1868 #28417971

order14944
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic1868

Splittings

SylowC467 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22D1868
commutator, cosocleC4×C467C23
FrattiniC4C22×D467
FittingC2×C8×C467C2
socle, prime radicalC22×C467D4
hypercenterC2×C8D467
hypocenterC467C2×Q16
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Conjugacy classes & character table

3742 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#44469840, #44469842, #44469852, …
maximal normal subgroup of#44469840, #44469842, #44469852, …
maximal quotient ofC2×#28417878, C2×#28417887, C4×Dic1868, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14944, 164);