Finite Group Databasebeta

#45689291

order33424
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC2089 ⋊ M16

Subgroups

subgroupG/H
center, FrattiniC2C2×#22552523
commutator, socleC2×C2089C2×C4
FittingC4×C2089C4
prime radicalC2×D2089C4
cosocleDic2089C22
hypercenterC4#22552523
hypocenterC2089M16
LCSG ▷ C2×C2089 ▷ C2089
UCSC1 ◁ C2 ◁ C4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16712

Polycyclic presentation:

2^4,2089|a^2=c,c^2=d,b^a=bd,e^a=e^1300,e^b=e^2088,e^c=e^2088

Conjugacy classes & character table

2098 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33424, 50);