Finite Group Databasebeta

#44415447

order29152
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC911 ⋊ #97

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D911
commutatorC2×C911C42
FittingC42×C911C2
socle, prime radicalC22×C911C2×C4
cosocleC2×C4×C911C22
hypercenterC42D911
hypocenterC911#97
LCSG ▷ C2×C911 ▷ C911
UCSC1 ◁ C2×C4 ◁ C42

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29152

Polycyclic presentation:

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

Conjugacy classes & character table

7300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29152, 57);