Finite Group Databasebeta

C2×#21418727 #28417958

order14944
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#21418727

Splittings

SylowC467 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D467
commutatorC2×C467C22×C4
FrattiniC4C22×D467
FittingC22×C4×C467C2
socleC22×C467C2×C4
prime radicalC23×C467C4
cosocleC4×C467C23
hypercenterC22×C4D467
hypocenterC467C2×M16
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C2×C4 ◁ C22×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7472

Conjugacy classes & character table

3748 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#44469793, C467⋊#338, #44469796, …
maximal normal subgroup of#44469793, C467⋊#338, #44469796, …
maximal quotient ofC2×#28417864, C4×#21418727, C2×C22⋊(C467⋊C8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14944, 151);