Finite Group Databasebeta

#44440714

order29408
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC919 ⋊ #108

Subgroups

subgroupG/H
centerC4C22⋊D919
commutatorC4×C919C2×C4
FrattiniC2×C4C2×D919
FittingM16×C919C2
socleC2×C919C4⋊C4
prime radicalC22×C919Q8
cosocleC2×C4×C919C22
hypercenterM16D919
hypocenterC919#108
LCSG ▷ C4×C919 ▷ C2×C919 ▷ C919
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14704

Polycyclic presentation:

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

Conjugacy classes & character table

4604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29408, 81);