Finite Group Databasebeta

#44440697

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

Aliases

No aliases for this group.

Splittings

SylowC919 ⋊ #101

Subgroups

subgroupG/H
centerC2(C2×D919)⋊C4
commutator, prime radicalC22×C919C2×C4
FrattiniC2×C4C2×D919
FittingM16×C919C2
socleC2×C919C22⋊C4
cosocleC2×C4×C919C22
hypercenterM16D919
hypocenterC919#101
LCSG ▷ C22×C919 ▷ C2×C919 ▷ C919
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14704

Polycyclic presentation:

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

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, 64);