Finite Group Databasebeta

#44415461

order29152
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC911 ⋊ #103

Subgroups

subgroupG/H
centerC22D3644
commutatorC4×C911C2×C4
FrattiniC2×C4C2×D911
FittingC2×C8×C911C2
socle, prime radicalC22×C911D4
cosocleC2×C4×C911C22
hypercenterC2×C8D911
hypocenterC911#103
LCSG ▷ C4×C911 ▷ C2×C911 ▷ C911
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29152

Polycyclic presentation:

2^5,911|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^910,c^b=ce,f^b=f^910

Conjugacy classes & character table

7294 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29152, 71);