Finite Group Databasebeta

#44440694

order29408
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC919 ⋊ #99

Subgroups

subgroupG/H
centerC2C22⋊Dic919
commutatorC22×C919C2×C4
FrattiniC23C2×D919
Fitting, prime radicalC2×D4×C919C2
socleC2×C919C22⋊C4
cosocleC23×C919C22
hypercenterC2×D4D919
hypocenterC919#99
LCSG ▷ C22×C919 ▷ C2×C919 ▷ C919
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7352

Polycyclic presentation:

2^5,919|a^2=d,b^a=bc,c^a=ce,f^a=f^918,d^b=de

Conjugacy classes & character table

4601 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29408, 61);