Finite Group Databasebeta

#44476207

order30304
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

FittingC42×C947 ⋊ C2
SylowC947 ⋊ #117

Subgroups

subgroupG/H
centerC2×C4C2×D947
commutatorC2×C947C22×C4
FrattiniC22C22×D947
FittingC42×C947C2
socle, cosocleC22×C947C23
prime radicalC22×D947C22
hypercenterC42D947
hypocenterC947#117
LCSG ▷ C2×C947 ▷ C947
UCSC1 ◁ C2×C4 ◁ C42

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15152

Polycyclic presentation:

2^5,947|a^2=e,c^2=d,b^a=bd,f^b=f^946

Conjugacy classes & character table

7588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30304, 103);