Finite Group Databasebeta

#26235283

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #22746

Subgroups

subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C8×Q8×C47C2
socleC22×C47C22×C4⋊C4
prime radicalC23×C47C22×Q8
cosocleC22×C4×C47C24
hypercenterC2×C8×Q8D47
hypocenterC47#22746
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ C2×C8×Q8

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|a^2=g,b^2=e,c^2=ef,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^46,d^b=de

Conjugacy classes & character table

1910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 188573);