Finite Group Databasebeta

#44499438

order30608
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC1913 ⋊ C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C2×D1913
commutatorC2×C1913C2×C4
FittingC2×C4×C1913C2
socle, prime radical, cosocleC22×C1913C22
hypercenterC2×C4D1913
hypocenterC1913C4⋊C4
LCSG ▷ C2×C1913 ▷ C1913
UCSC1 ◁ C22 ◁ C2×C4

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30608

Polycyclic presentation:

2^4,1913|a^2=d,b^2=c,b^a=bc,e^b=e^1912

Conjugacy classes & character table

7658 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30608, 19);