Finite Group Databasebeta

#44472194

order29984
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC937 ⋊ SD32

Subgroups

subgroupG/H
centerC2#28418279
commutator, cosocleC8×C937C22
FrattiniC8C2×D937
Fitting, prime radicalD8×C937C2
socleC2×C937D8
hypercenterD8D937
hypocenterC937SD32
LCSG ▷ C8×C937 ▷ C4×C937 ▷ C2×C937 ▷ C937
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D8

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14992

Polycyclic presentation:

2^5,937|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^936,c^b=cd,d^b=de

Conjugacy classes & character table

3287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29984, 90);