Finite Group Databasebeta

#37587702

order24496
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1531 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D1531
commutator, cosocleC4×C1531C22
FrattiniC4C2×D1531
Fitting, prime radicalD4×C1531C2
socleC2×C1531D4
hypercenterD4D1531
hypocenterC1531SD16
LCSG ▷ C4×C1531 ▷ C2×C1531 ▷ C1531
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12248

Polycyclic presentation:

2^4,1531|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1530,c^b=cd

Conjugacy classes & character table

3832 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24496, 28);