Finite Group Databasebeta

#28414185

order14752
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC461 ⋊ C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22C2×#14270406
commutatorC2×C461C2×C8
FittingC2×C4×C461C4
socle, prime radicalC22×C461C2×C4
cosocleC2×Dic461C22
hypercenterC2×C4#14270406
hypocenterC461C4⋊C8
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C22 ◁ C2×C4

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Polycyclic presentation:

2^5,461|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^48,f^b=f^460,f^d=f^460

Conjugacy classes & character table

940 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#44442934, #44442935, #44442936, …
maximal normal subgroup of#44442934, #44442935, #44442936, …
maximal quotient of#44442938, #44442940, #44442942, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14752, 213);