Finite Group Databasebeta

#39907407

order26032
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1627 ⋊ M16

Subgroups

subgroupG/H
center, FrattiniC4C2×D1627
commutator, socleC2×C1627C2×C4
FittingC2×C4×C1627C2
prime radicalC22×C1627C4
cosocleC4×C1627C22
hypercenterC2×C4D1627
hypocenterC1627M16
LCSG ▷ C2×C1627 ▷ C1627
UCSC1 ◁ C4 ◁ C2×C4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13016

Polycyclic presentation:

2^4,1627|a^2=c,c^2=d,b^a=bd,e^a=e^1626

Conjugacy classes & character table

6514 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26032, 24);