Finite Group Databasebeta

#28417870

order14944
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #100

Subgroups

subgroupG/H
centerC2C22⋊Dic467
commutatorC22×C467C2×C4
FrattiniC2×C4C2×D467
Fitting, prime radicalC2×D4×C467C2
socleC2×C467C22⋊C4
cosocleC2×C4×C467C22
hypercenterC2×D4D467
hypocenterC467#100
LCSG ▷ C22×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3736

Polycyclic presentation:

2^5,467|a^2=d,d^2=e,b^a=bc,c^a=ce,f^a=f^466,d^b=de

Conjugacy classes & character table

2341 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#44469823, #44469824, #44469826, …
maximal normal subgroup of#44469823, #44469824, #44469826, …
maximal quotient of#44469761, #44469777, #44469781, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14944, 63);